Question

一个袋子最初只含红色和蓝色弹珠，且蓝色比红色多。向袋中加入红色弹珠，直到蓝色弹珠只占袋中弹珠的 $\tfrac{1}{3}$ 。然后加入黄色弹珠，直到蓝色弹珠只占袋中弹珠的 $\tfrac{1}{5}$ 。最后，将袋中蓝色弹珠的数量加倍。现在袋中弹珠有几分之几是蓝色？

A bag initially contains red marbles and blue marbles only, with more blue than red. Red marbles are added to the bag until only $\tfrac{1}{3}$ of the marbles in the bag are blue. Then yellow marbles are added to the bag until only $\tfrac{1}{5}$ of the marbles in the bag are blue. Finally, the number of blue marbles in the bag is doubled. What fraction of the marbles now in the bag are blue?

$\dfrac{1}{5}$

$\dfrac{1}{4}$

$\dfrac{1}{3}$

$\dfrac{2}{5}$

$\dfrac{1}{2}$

答案：C

知识点：分数比与比例

难度评级：1240

解答：

设蓝色弹珠数为 $B$ 。加入红色弹珠后，总数为 $3B$ ；加入黄色弹珠后，总数为 $5B$ ，蓝色仍为 $B$ 。

将蓝色弹珠数量加倍后，有 $2B$ 个蓝色弹珠，总数变为 $6B$ ，所以蓝色所占比例为 $\dfrac{2B}{6B} = \dfrac{1}{3}$ 。

所以正确答案是 C。

Let there be $B$ blue marbles. After adding red marbles the total is $3B;$ after adding yellow marbles the total is $5B,$ still with $B$ blue.

Doubling the blue marbles gives $2B$ blue out of $6B$ total, which is $\dfrac{2B}{6B} = \dfrac{1}{3}.$

Thus, the correct answer is C.

2004 AMC 10B 第 14 题

答案：C

难度评级：1240

解答：

其他年份的第 14 题